Geodesic
Non-asymptotic analysis of Lawley--Hotelling statistic for high dimensional data
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 178-189

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We consider General Linear Model (GLM) that includes multivariate analysis of variance (MANOVA) and multiple linear regression as special cases. In practice, there are several widely used criteria for GLM: Wilks’ lambda, Bartlett–Nanda–Pillai test, Lawley–Hotelling test and Roy maximum root test. Limiting distributions for the first three mentioned tests are known under different asymptotic settings. In the present paper we get the computable error bounds for normal approximation of Lawley–Hotelling statistic when dimensionality grows proportionally to sample size. This result enables us to get more precise calculations of the p-values in applications of multivariate analysis. In practice, more and more often analysts encounter situations when the number of factors is large and comparable with the sample size. Examples include medicine, biology (i.e., DNA microarray studies) and finance. 
@article{ZNSL_2019_486_a9,
     author = {A. A. Lipatev and V. V. Ulyanov},
     title = {Non-asymptotic analysis of {Lawley--Hotelling} statistic for high dimensional data},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {178--189},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a9/}
}
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A. A. Lipatev; V. V. Ulyanov. Non-asymptotic analysis of Lawley--Hotelling statistic for high dimensional data. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 178-189. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a9/